This invention relates to dispersion managed fibers and, in particular, to dispersion managed fibers which exhibit reduced sensitivity to manufacturing variabilities, have relatively small changes in mode field diameter (MFD) at the junctions between fiber sections having positive dispersions and fiber sections having negative dispersions, and/or are readily manufactured using the xe2x80x9ctabletxe2x80x9d method.
A. Dispersion Managed Fibers
Dispersion managed fibers are optical fibers which have a low to zero net dispersion by purposely incorporating, along the axial length of the fiber, sections that have a positive dispersion and sections that have a negative dispersion.
The discovery of dispersion managed fibers arose, at least in part, from the realization that transmission of light at high bit rates ( greater than 40 Gbs) requires not only handling linear impairment but also non-linear impairments. Initial work was done on understanding how dispersion management helped NRZ transmission. However, very soon it was realized that this concept applied equally well to other forms of data transmission (soliton, RZ, etc.).
Dispersion management has been proposed at various length scales, in the 100""s of meters range and in the 10""s of kilometers range, with names such as xe2x80x9cdispersion managed fibersxe2x80x9d used to refer to management in the 100""s of meters range and xe2x80x9cdispersion managed cablexe2x80x9d referring to management on the 10""s of kilometers range. For ease of discussion, the terminology xe2x80x9cdispersion managed fiberxe2x80x9d is used herein for both ranges.
In broadest outline, dispersion management achieves global near net zero dispersion while still having finite local dispersion. That is, by controlling the product of the length (Li) and dispersion (Di) of the individual fiber sections, the sum of those products for the entire fiber (xcexa3Lixc2x7Di) can be made small, thus giving the fiber the desired low to zero net dispersion. As used herein, the sum of the Lixc2x7Di products for a dispersion managed fiber is referred to as the fiber""s xe2x80x9coverallxe2x80x9d dispersion.
A key advantage of using fiber sections having substantial local dispersions (substantial Di values) is the avoidance of the adverse consequences of various non-linear effects, including four wave mixing. By avoiding these problems, higher power densities can be propagated in dispersion managed fibers than in conventional low dispersion fibers. This is an important advantage in terms of increasing the transmitted bit rate, the repeater spacing, and the total system length. It should be noted that these improvements in fiber performance are achieved irrespective of the transmission format, e.g., the improvements in performance are achieved for NRZ, RZ, and soliton transmission.
In addition to making the sum of the Lixc2x7Di products small, for fibers which are to carry signals at a plurality of wavelengths, i.e., WDM fibers, it is also important to control the change in dispersion with wavelength (dD/dxcex) for the fiber (referred to hereinafter as the xe2x80x9cdispersion slopexe2x80x9d or xe2x80x9cSxe2x80x9d). More particularly, a dispersion managed fiber which is to be used in a WDM setting needs to have sections whose individual slopes (Si) are controlled so that xcexa3Lixc2x7Si is close to or preferably equal to zero for the entire fiber.
The combination of the requirement that xcexa3Lixc2x7Di is approximately equal to zero and that xcexa3Lixc2x7Si is also approximately equal to zero, means that the ratio of Di to Si needs to be substantially the same for each section.
In addition to the foregoing, for very high bit rates, the variation in Di within a section (i.e., Di(l) where l is length along the fiber axis within a section) also becomes important. Specifically, if the variation in Di(l) is large, the non-linear effects which dispersion management is designed to address can still have an adverse effect on individual bits. That is, the system""s xe2x80x9cQxe2x80x9d value can be considerably reduced even though the average properties are well controlled over the whole system length.
A discussion of dispersion managed fibers, including the effects of local variations in dispersion, can be found in Anis et al., xe2x80x9cContinuous Dispersion Managed Fiber For Very High Speed Soliton Systems,xe2x80x9d ECOC""99 Proceedings, Vol. 1, pages 230-232, 1999, and the references referred to therein, all of which are incorporated herein by reference.
B. The Problem of Process Variabilities in the Manufacture of Dispersion Managed Fibers
Dispersion managed fibers can be manufactured in various ways known in the art. As with any manufacturing process, the processes used in making dispersion managed fibers result in at least some variations in the product due to process variabilities. As discussed above, the entire concept of dispersion management is based on tight control of both global and local dispersion, as well as dispersion slope. Accordingly, dealing with the problem of process variabilities is especially important in the area of dispersion managed fibers.
As described in detail below, in accordance with the invention, certain fiber profiles have been discovered which satisfy the optical properties needed for a dispersion managed fiber and which are significantly less sensitive to process variations. Such profiles allow for the manufacture of dispersion managed fibers with improved overall properties compared to those previously known in the art.
C. Fracture Problems Associated with the xe2x80x9cTabletxe2x80x9d Method of Manufacturing Dispersion Managed Fibers
A particularly efficacious approach to making dispersion managed fibers involves the use of individual xe2x80x9ctabletsxe2x80x9d having the desired dispersion properties which are assembled together to form an entire fiber. A description of this process can be found in commonly assigned, co-pending, U.S. patent application Ser. No. 08/844,997, filed Apr. 23, 1997, and entitled xe2x80x9cMethod of Making Optical Fibers,xe2x80x9d the contents of which are incorporated herein by reference. This application was published as PCT Patent Publication No. WO97/41076 on Nov. 6, 1997.
The tablets used in this process tend to suffer from fracturing problems during manufacture. These tablets are formed from a core cane (i.e., a cane containing the core of the fiber and some cladding) by various cutting techniques, including scoring/snapping, laser cutting, water jet cutting, saw cutting, and the like. After cutting, the transverse surfaces of the tablet may be polished if desired.
In accordance with a further aspect of the invention, it has been discovered that the fracturing observed during the cutting of tablets is due to residual stresses introduced into the core cane by prior processing steps. Surprisingly, it has been found that the same types of profiles which reduce sensitivities to processing variabilities, also solve the fracturing problem.
It should be noted that the profiles of the invention which reduce sensitivities to processing variabilities can be used with manufacturing techniques which do not involve the cutting of tablets and thus do not have the fracturing problem.
In view of the foregoing, it is an object of the invention to provide fiber profiles for use in dispersion managed fibers which exhibit reduced sensitivities to manufacturing variabilities. More particularly, it is an object of the invention to provide dispersion managed fibers having a plurality of sections wherein the standard deviation of the dispersion values for the sections is reduced compared to prior dispersion managed fibers. It is also an object of the invention to provide sections whose dispersion values exhibit less variation along the length of a section.
It is another object of the invention to provide fiber profiles which lead to relatively small changes in mode field diameter (MFD) at the junctions between the positive and negative dispersion sections of a dispersion managed fiber. The problems associated with mode field diameter mismatches at such junctions are discussed below.
It is an additional object of the invention to provide profiles for core canes which are less subject to fracture when cut into tablets than prior art profiles.
To achieve these and other objects, the invention in accordance with a first aspect provides an optical waveguide fiber for use in a dispersion managed optical communication system comprising a core of transparent material surrounded by a cladding of transparent material having a refractive index ncl, said core comprising three radially adjacent regions which in order of increasing radius are:
(a) a central core region having:
(i) a maximum index of refraction nc such that xcex94c% is greater than zero and less than about 1.2, where xcex94c%=100xc2x7(nc2xe2x88x92ncl2)/2ncl; and
(ii) an alpha profile with an alpha value less than about 2.3;
(b) a moat region having a minimum index of refraction nm such that xcex94m% is less than or equal to xe2x88x920.3, where xcex94m%=100xc2x7(nm2xe2x88x92ncl2)/2ncl, said moat region comprising, in order of increasing radius, first, second, third, and fourth radially adjacent regions (also referred to herein as xe2x80x9csub-regionsxe2x80x9d) wherein:
(i) the index of refraction decreases throughout the first sub-region;
(ii) the index of refraction increases substantially linearly in the second sub-region;
(iii) the index of refraction increases substantially linearly in the fourth sub-region; and
(iv) the third sub-region is a transition region which smoothly connects the third and fourth substantially linear sub-regions; and
(c) a ring region having a maximum refractive index nr such that xcex94r% is greater than zero and less than +0.5, where xcex94r%=100xc2x7(nr2xe2x88x92ncl2)/2ncl.
As used herein, ccl is the minimum value of the index of refraction in the cladding of the fiber.
In accordance with a second aspect of the invention, xcex94m% satisfies the following relationships:
xcex94m%xe2x89xa6xe2x88x920.55 for Rc/Rm less than 0.6;
xcex94m%xe2x89xa6xe2x88x920.50 for Rc/Rm less than 0.45;
xcex94m%xe2x89xa6xe2x88x920.45 for Rc/Rm less than 0.4; or
xcex94m%xe2x89xa6xe2x88x920.30 for Rc/Rm less than 0.3;
where Rc is the outer radius of the central core region and Rm is the outer radius of the moat region:
In accordance with a third aspect, the invention provides dispersion managed optical waveguide fibers composed of at least one section having a positive dispersion and at least one section having a negative dispersion, wherein the fiber and/or the sections have some and preferably all of the following properties:
(1) the overall dispersion of the fiber (i.e., the sum of the of the Lixc2x7Di products) is less than 1 ps/nm-km,
(2) the magnitude of the dispersion slope for each section of the fiber is less than 0.04 ps/nm2-km,
(3) the standard deviation of the dispersion values for fiber sections having negative dispersions is less than 0.5 ps/nm-km,
(4) the difference between the maximum and minimum values of the magnitude of the dispersion over the length of those sections of fiber which have a negative dispersion is less than 0.5 ps/nm-km,
(5) the standard deviation of the dispersion values for fiber sections having positive dispersions is less than 0.3 ps/nm-km,
(6) the difference between the maximum and minimum values of the magnitude of the dispersion over the length of those sections of the fiber having a positive dispersion is less than 0.3 ps/nm-km, and/or
(7) the average of the mode field diameters of the fiber sections having positive dispersions differs from the average of the mode field diameters of the sections having negative dispersions by less than 10 microns and preferably by less than 6 microns.
The standard deviations referred to in properties (3) and (5) are determined by obtaining dispersion values for fiber sections of a population of fibers, e.g., at least ten fibers, and then computing the standard deviation from the following formula, where the xi""s are the dispersion values, {overscore (x)} is the average of the dispersion values, and N is the total number of values:       S    .    D    .    =      σ    =                            1          N                ⁢                              ∑                          i              =              1                        N                    ⁢                                    (                                                x                  1                                -                                  x                  _                                            )                        2                              
This formula is used irrespective of the distribution of the data points, e.g., the formula is used even if the data is not normally distributed.
Dispersion values can be calculated from measured group delay in various ways known to the art. For example, interferometry techniques, details of which can be found in EIA/TIA-455-169A (FOTP-169) xe2x80x9cChromatic dispersion measurements of single mode optical fibers by phase shift method,xe2x80x9d or four wave mixing techniques as described in L. F. Mollenauer, P. V. Mamyshev and M. J. Neubelt, xe2x80x9cMethod for facile and accurate measurement of optical fiber dispersion maps,xe2x80x9d Optics Letters, Vol 21, No. 21, Nov. 15, 1996, can be used. Either technique can be used to calculate both positive and negative dispersions. The interferometry technique generally has better spatial resolution, while the four-wave mixing technique has better dispersion resolution. In particular, by averaging over many measurements, the interferometry technique can be used to calculate dispersion values over fiber lengths less 100 m. On the other hand, using the four-wave mixing technique one can obtain dispersion values having a resolution less than 0.1 ps/nm-km for fiber lengths greater than 500 m. Hence, using a combination of these two techniques, one can reliably obtain dispersion values for fiber lengths less than 500 m.
Measurement of group delay at various wavelengths allows one to compute the dispersion by taking the derivative of the group delay measurement with respect to wavelength. Dispersion slope can then be obtained by taking the derivative of the computed dispersion with respect to wavelength. Usually, instead of taking derivatives of numerical values, fitting routines are used to fit the measured group delay and then the dispersion and the dispersion slope are calculated analytically by taking derivatives of the fit to the group delay data with respect to wavelength. The group delay data is preferably obtained using the measurement techniques described in the previous paragraph.
Mode field diameter is determined using Petermann""s second definition of the mode field diameter in the near field. See K. Petermann, Electronic Letters, 1983, Vol. 19, pp. 712-714. The reference measurement method for mode-field diameter is the variable aperture method in the far field (VAMFF). Petermann""s second definition of the mode-field diameter is a mathematical model which does not assume a specific shape for the distribution. This near field definition is related to the far field by the Hankel transform. Pask""s transformation of Petermann""s definition of the mode-field diameter is applied directly to the two-dimensional far field data through a numerical integration routine. See C. Pask, Electronic Letters, 1984, Vol 20, pp. 144-145. The Petermann mode-field diameter in the near field is calculated from the far field rms width.
The index of refraction profiles of fibers and/or fiber sections having the properties listed above are preferably those described above in accordance with the first and second aspects of the invention. However, other profiles can be used if desired. In general terms, the shape of the refractive index profile in any of the regions or sub-regions making up the overall profile may be selected from the group consisting of an xcex1-profile, a step, a rounded step, a trapezoid, and a rounded trapezoid.
In accordance with a fourth aspect of the invention, a method of reducing the variation in dispersion of an optical waveguide fiber due to manufacturing variabilities is provided which comprises:
(a) selecting a profile for the fiber which comprises a central core region, a moat region, and a ring region, wherein the central core region has an alpha profile with an alpha value of less than about 2.3; and
(b) manufacturing a fiber which substantially has the profile selected in step (a);
wherein the fiber manufactured in step (b) has:
(i) a dispersion slope whose magnitude is less than 0.04 ps/nm2-km; and
(ii) a dispersion the magnitude of which varies along the length of the fiber, the difference between the maximum and the minimum of said magnitude over said length being less than 0.5 ps/nm-km.
In accordance with a fifth aspect of the invention, a method of producing tablets from a silica core cane is provided which comprises:
(a) providing a silica core cane having a cladding which has an index of refraction ncl, said silica core cane having an index of refraction profile which comprises a central core region, a moat region, and a ring region, wherein:
(i) both the central core region and the ring region are doped substantially only with germanium;
(ii) the moat region is doped substantially only with fluorine and has a minimum index of refraction nm such that xcex94m% less than 0 where xcex94m%=100xc2x7(nm2xe2x88x92ncl2)/2ncl; and
(iii) the central core region has an alpha profile with an alpha value of less than about 2.3; and
(b) cutting a plurality of tablets from the core cane.
Tablets made in this way exhibit less fracturing than tablets cut from a comparable core cane having a central core region whose alpha value is greater than 4.
In accordance with certain preferred embodiments of the invention, at least some of the fiber sections having positive dispersions have a profile P+(r), where r is radial distance from the center of the fiber, at least some of the fiber sections having negative dispersions have a profile Pxe2x88x92(rxe2x80x2), where rxe2x80x2 is radial distance from the center of the fiber, P+ and Pxe2x88x92 are substantially the same, and rxe2x80x2="xgr"r, where "xgr" is a constant which may be greater or less than 1.0. Put another way, in accordance with these embodiments, substantially the same profile shape is used for negative and positive dispersion sections, with the type of dispersion exhibited by a section being determined through adjustments in the scale of its profile, e.g., by adjustments in the over-clad diameter of the preform used to produce the section.
FIG. 1 illustrates particularly preferred refractive index profiles for the optical waveguide fibers and fiber sections of the invention. The reference numbers used in this figure correspond to the following:
10 central core region which is substantially centered about the symmetry line of the fiber;
11, 12, 13, 14 first, second, third, and fourth sub-regions of the moat region; and
15a, 15b, 15c representative examples of suitable, alternate profiles for the ring region.
Preferred values for the parameters Rc, Rm, Rr, xcex94c%, xcex94m%, and xcex94r% are set forth in Table 1. Central core region 10 preferably has an alpha profile. As known in the art, an alpha profile can be defined by the equation:
xcex94(r)%=xcex94(ro)%xc2x7(1xe2x88x92[|rxe2x88x92ro|/(r1xe2x88x92ro)]xcex1),
where ro is the maximum point of the profile, r1 is the point at which xcex94(r)% is zero, r is in the range rixe2x89xa6rxe2x89xa6rf, ri is the initial point of the xcex1-profile, rf is the final point of the xcex1-profile, and xcex1 is an exponent which is a real number. In accordance with the preferred embodiments of the invention, xcex1 is less than about 2.3, and preferably is about 2.0. Most preferably, xcex1 is greater than about 1.5.
As shown in FIG. 1, the core consists of just the central core region, the moat region, and the ring region. As also shown in FIG. 1, the moat region consists of just the first, second, third, and fourth sub-regions. These configurations, whether used in combination as shown in FIG. 1 or used separately, represent preferred forms for the core and the moat region.
The refractive index profile shown in FIG. 1 is designed to provide a particular power distribution of signal light propagating in the waveguide fiber. It is this power distribution that results in the waveguide fiber having a desired dispersion and dispersion slope over a pre-selected range of wavelengths. At the same time, the power distribution of light signals propagating in the waveguide is controlled to provide such characteristics as single mode operation above a pre-selected wavelength (although various aspects of the invention are not limited to single mode waveguides), low attenuation (e.g., an attenuation no greater than about 0.34 dB/km at, for example, 1550 nm and preferably less than 0.25 dB/km), and a properly placed zero dispersion wavelength. A preferred pre-selected wavelength range is from about 1500 nm to about 1700 nm (most preferably from 1520 nm to 1650 nm) and a preferred zero dispersion wavelength is less than about 1400 nm, although the principles of the invention can be applied to other wavelength ranges and other zero dispersion wavelengths if desired.